Difference between revisions of "Team:Queens Canada/Model"

 
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<img src="https://2017.igem.org/Special:UploadStash/thumb/1521h12p2w2k.bv8i1y.919.jpg/120px-1521h12p2w2k.bv8i1y.919.jpg" length=100 width=400>
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<div class="column full_size judges-will-not-evaluate">
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p.big {
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<h3>★  ALERT! </h3>
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line-height: 200%;
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<p>This page is used by the judges to evaluate your team for the <a href="https://2017.igem.org/Judging/Medals">medal criterion</a> or <a href="https://2017.igem.org/Judging/Awards"> award listed above</a>. </p>
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<p> Delete this box in order to be evaluated for this medal criterion and/or award. See more information at <a href="https://2017.igem.org/Judging/Pages_for_Awards"> Instructions for Pages for awards</a>.</p>
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width:70px;
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position:fixed;
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bottom:12%;
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z-index:11;
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function myFunction(id) {
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    var x = document.getElementById(id);
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    if (x.className.indexOf("w3-show") == -1) {
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        x.className += " w3-show";
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<img src="https://static.igem.org/mediawiki/2017/0/07/T--Queens_Canada--TheoryBanner.jpg">
 
</div>
 
</div>
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<div class="clear"></div>
 
  
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<div class="column full_size">
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<div style="height:30px;width:100%">
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<h1> Modeling</h1>
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<img src="https://static.igem.org/mediawiki/2017/6/64/T--Queens_Canada--NavyNavBackground1.jpg" style="width:100%;height:30px">
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</div>
  
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<p>Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab.</p>
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<div style="background-color:#afbee8;color:white;padding:500px 150px 50px 150px;">
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<center>
  
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<p class="big"><font size="12" color="black" face="Corbel">The mathematical modeling theory outlined on this page was integrated in the creation of our application, to ensure reliable results. </font></p></center>
 +
<br>
 
</div>
 
</div>
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<div class="clear"></div>
 
  
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<div class="column half_size">
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<div style="height:30px;width:100%">
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<h3> Gold Medal Criterion #3</h3>
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<img src="https://static.igem.org/mediawiki/2017/6/64/T--Queens_Canada--NavyNavBackground1.jpg" style="width:100%;height:30px">
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<p>
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</div>
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To complete for the gold medal criterion #3, please describe your work on this page and fill out the description on your <a href="https://2017.igem.org/Judging/Judging_Form">judging form</a>. To achieve this medal criterion, you must convince the judges that your team has gained insight into your project from modeling. You may not convince the judges if your model does not have an effect on your project design or implementation.
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−
</p>
+
  
−
<p>
+
 
−
Please see the <a href="https://2017.igem.org/Judging/Medals"> 2017 Medals Page</a> for more information.  
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−
</p>
+
 
 +
<div style="background-color:#afbee8;color:white;padding:50px 150px 50px 150px;">
 +
<div class="w3-container" style="padding:5px;width:100%;">
 +
 
 +
<button onclick="myFunction('Demo1')" class="myButton" style="color:#171A3D;width:100%;">Relating Relative Promoter Units to Transcription Rate</button>
 +
<div id="Demo1" class="w3-container w3-hide">
 +
<div style="background-color:#afbee8;color:white;padding:50px 150px 50px 150px;">
 +
<h1><font color="black" face="Arial"><center><span style="font-weight:normal; font-size: 23pt">Relating Relative Promoter Units to Transcription Rate</span></center></font></h1><hr/>
 +
<br>
 +
 
 +
<p align="left"><font size="5" color="black" style="Corbel">
 +
<em><u> Assumption: </em></u><br></p>
 +
<p align="left"><font size="5" color="black" style="Corbel">
 +
The first major assumption, is declaring <em>"Promoter Activity" </em>, to be a direct model of transcription rate. "Promoter Activity" is the number of RNAP molecules that clear the final base pair of a promoter (with units of [PoPS]
 +
= Polymerase per second).</p>
 +
<p align="left"><br>Thus,<br>
 +
<img src="https://static.igem.org/mediawiki/2017/b/b9/T--Queens_Canada--RPUEquation1.png" style = "width:40%"><br>
 +
Where, <br>
 +
<img src="https://static.igem.org/mediawiki/2017/d/db/T--Queens_Canada--PoPSEquation2.png" style = "width:20%"><br>
 +
Thus, through simple substitution: <br>
 +
<img src="https://static.igem.org/mediawiki/2017/4/48/T--Queens_Canada--RPUEquationallvariables.png" style = "width:60%"><br>
 +
<br><br><br></font></p></center>
 +
 
 +
<p align="left" style="line-height:1.5;"><font size="5" style="corbel" color="black">
 +
The modelling can further be simplified through a series of assumptions: <br>
 +
1) GFP expressed from test and standard promoters, have equivalent maturation rates, as they mature under the same conditions: <br>
 +
<img src="https://static.igem.org/mediawiki/2017/a/ae/T--Queens_Canada--alphaassumptionEq.png" style="width:13%">
 +
<br><br>
 +
2) Since both the test and standard promoters are carried on the same plasmid backbone, assume they have the same average copy number: <br>
 +
<img src="https://static.igem.org/mediawiki/2017/f/f5/T--Queens_Canada--avgCopyNumberEq.png" style="width:13%"><br> <br>
 +
3) Since promoters have been standardized to have identical transcription initiation sites (predicted) and identical sequences downstream of the site, we expect them to produce the same mRNA sequences.<br>
 +
Therefore,<br>
 +
Expect transcribed mRNA to be identical, implying mRNA degradation rates are equivalent: <br>
 +
<img src="https://static.igem.org/mediawiki/2017/d/d0/T--Queens_Canada--mRNADegRateEq.png" style="width:13%"> <br><br>
 +
Thus, we assume translational rates of immature GFP from some mRNA are equal: <br>
 +
<img src="https://static.igem.org/mediawiki/2017/8/8a/T--Queens_Canada--proteinDegRateEq.png" style="width:13%"><br><br>
 +
4) Assume that immature GFP is stable. Therefore, protein degradation is negligable compared to dilution due to cell growth. <br>
 +
Thus: <br>
 +
<img src="https://static.igem.org/mediawiki/2017/7/74/T--Queens_Canada--dilutionRateEq.png" style="width:13%"><br>
 +
 
 +
Thus, <br>
 +
<img src="https://static.igem.org/mediawiki/2017/2/2b/T--Queens_Canada--RPUEquation2.png" style="width:40%"><br>
 +
and if<br> <img src="https://static.igem.org/mediawiki/2017/b/b3/T--Queens_Canada--lessthanalphaEq.png" style="width:13%"><br>
 +
Then, <br>
 +
<img src="https://static.igem.org/mediawiki/2017/7/73/T--Queens_Canada--alphaapproximation.png" style="width:10%"><br>
 +
<br>
 +
Therefore, we assume the difference between growth rates of cells containing the test promoter construct and cells containing the standard promoter construct, is negligible compared to the maturation rate of GFP. <br><br><hr><br>
 +
Thus, for the purposes of QGEM's modelling; <br>
 +
<img src="https://static.igem.org/mediawiki/2017/a/ac/T--Queens_Canada--RPUFinal.png" style="width:40%">
 +
</font></p>
 +
<br>
 +
 
 +
</div>
 +
<div style="height:30px;width:100%">
 +
<img src="https://static.igem.org/mediawiki/2017/6/64/T--Queens_Canada--NavyNavBackground1.jpg" style="width:100%;height:30px">
 
</div>
 
</div>
 +
</div></div>
  
−
<div class="column half_size">
 
−
<h3>Best Model Special Prize</h3>
 
  
−
<p>
+
 
−
To compete for the <a href="https://2017.igem.org/Judging/Awards">Best Model prize</a>, please describe your work on this page  and also fill out the description on the <a href="https://2017.igem.org/Judging/Judging_Form">judging form</a>. Please note you can compete for both the gold medal criterion #3 and the best model prize with this page.  
+
<div class="w3-container" style="padding:5px">
 +
<button onclick="myFunction('Demo2')" class="myButton" style="color:#171A3D;width:100%;">Relating Transcription Rate to Protein Production</button>
 +
<div id="Demo2" class="w3-container w3-hide">
 +
<div style="background-color:#afbee8;color:white;padding:50px 150px 50px 150px;">
 +
<h1><font color="black" face="Arial"><center><span style="font-weight:normal; font-size: 23pt">Relating Transcription Rate to Proteins Produced</span></center></font></h1><hr/>
 +
<br>
 +
 
 +
<u><em>Assumption:</u></em><br>
 +
CsgA alone and CsgA-fusions (such as CsgA-AFP8 and CsgA-SpyTag) behave similarly in terms of transcription in the cells.
 
<br><br>
 
<br><br>
−
You must also delete the message box on the top of this page to be eligible for the Best Model Prize.
+
The transcription rate of the CsgA gene is modeled as follows:
−
</p>
+
<br>
 +
<img src="https://static.igem.org/mediawiki/2017/e/e1/T--Queens_Canada--TranscriptionRateofCsgAgene.png" style="width:35%">
 +
<br>
 +
where, <br>
 +
<img src="https://static.igem.org/mediawiki/2017/a/af/T--Queens_Canada--ProductionRateofCsgAgenecropped.png" style="width:25%"><br>
 +
  <img src="https://static.igem.org/mediawiki/2017/0/0d/T--Queens_Canada--DegradationRateofCsgAgene.png" style="width:25%"><br>
 +
<br>
 +
Thus, by the stated assumption, the transcription rate of CsgA-fusions can be modeled with the same equation.  
 +
</font></p>
 +
<br>
 +
</div>
 +
<div style="height:30px;width:100%">
 +
<img src="https://static.igem.org/mediawiki/2017/6/64/T--Queens_Canada--NavyNavBackground1.jpg" style="width:100%;height:30px">
 +
</div>
 +
</div></div>
  
 +
 +
<div class="w3-container" style="padding:5px">
 +
<button onclick="myFunction('Demo3')" class="myButton" style="color:#171A3D;width:100%;">Relating RBS Strength to Translation Rate</button>
 +
<div id="Demo3" class="w3-container w3-hide">
 +
 +
<div style="background-color:#afbee8;color:white;padding:50px 150px 50px 150px;">
 +
 +
<h1><font color="black" face="Arial"><center><span style="font-weight:normal; font-size: 23pt">RBS Strength to Translation Rate</span></center></font></h1><hr/>
 +
<br>
 +
<p class="big"><font size="5" color="black" face="Corbel">
 +
Altering the RBS strength of the ribosome binding site in a plasmid, can be completed by altering the genetic makeup of the RBS. This was modeled through the utilization of the <a href="https://salislab.net/software/">RBS Calculator</a> created by Dr. Howard Salis, at Penn State University. Using the forward implementation of the calculator, one input's their protein coding sequence, organism, and target translation initiation rate. The calculator then outputs the RBS sequence required to achieve such a translation initiation rate under the conditions outlined.
 +
</div>
 +
<div style="height:30px;width:100%">
 +
<img src="https://static.igem.org/mediawiki/2017/6/64/T--Queens_Canada--NavyNavBackground1.jpg" style="width:100%;height:30px">
 
</div>
 
</div>
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<div class="clear"></div>
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</div></div>
  
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<div class="column full_size">
 
−
<h5> Inspiration </h5>
 
−
<p>
 
−
Here are a few examples from previous teams:
 
−
</p>
 
−
<ul>
 
−
<li><a href="https://2016.igem.org/Team:Manchester/Model">Manchester 2016</a></li>
 
−
<li><a href="https://2016.igem.org/Team:TU_Delft/Model">TU Delft 2016  </li>
 
−
<li><a href="https://2014.igem.org/Team:ETH_Zurich/modeling/overview">ETH Zurich 2014</a></li>
 
−
<li><a href="https://2014.igem.org/Team:Waterloo/Math_Book">Waterloo 2014</a></li>
 
−
</ul>
 
  
 +
<div class="w3-container" style="padding:5px">
 +
<button onclick="myFunction('Demo4')" class="myButton" style="color:#171A3D;width:100%;">Relating Translation Rate to Proteins Produced</button>
 +
<div id="Demo4" class="w3-container w3-hide">
 +
<div style="background-color:#afbee8;color:white;padding:50px 150px 50px 150px;">
  
 +
<h1><font color="black" face="Arial"><center><span style="font-weight:normal; font-size: 23pt">Translation Rate to Proteins Produced</span></center></font></h1><hr/>
 +
<br>
 +
<p class="big"><font size="5" face="Corbel" color="black"> The effect translation rate has on the protein production, was accounted for in the Salis Lab RBS Calculator Code. Thus, by simply declaring the desired translation initiation rate, the code properly took into account the impacts on protein production.
 
</div>
 
</div>
 +
<div style="height:30px;width:100%">
 +
<img src="https://static.igem.org/mediawiki/2017/6/64/T--Queens_Canada--NavyNavBackground1.jpg" style="width:100%;height:30px">
 +
</div>
 +
</div></div>
  
−
</html>
+
 
 +
<div class="w3-container" style="padding:5px">
 +
<button onclick="myFunction('Demo5')" class="myButton" style="color:#171A3D;width:100%;">Maximum Threshold of Secretion</button>
 +
<div id="Demo5" class="w3-container w3-hide">
 +
<div style="background-color:#afbee8;color:white;padding:50px 150px 50px 150px;">
 +
 
 +
<h1><font color="black" face="Arial"><center><span style="font-weight:normal; font-size: 23pt">Is There a Maximum Threshold of Secretion?</span></center></font></h1><hr/>
 +
<br>
 +
<br>
 +
 
 +
<p class="big"><font size="6" color="black" face="Corbel">
 +
<em> Is diffusion the rate limiting step? Do CsgA pile up in the cell? </em><br>
 +
<br></font></p>
 +
 
 +
<p class="big"><font size="5" color="black" face="Corbel">
 +
After 1 second, a spherical particle of radius 10 nanometers, has a displacement of 6.6 micrometers due to Brownian motion in water at room temperature. Determined via; <br>
 +
<img src="https://static.igem.org/mediawiki/2017/1/18/T--Queens_Canada--BrownianMotion.png" style="width:13%"><br>
 +
<br>
 +
Assuming this model represents movement of CsgA, diffusion is not the rate limiting step.
 +
</font></p>
 +
<br>
 +
</div>
 +
<div style="height:30px;width:100%">
 +
<img src="https://static.igem.org/mediawiki/2017/6/64/T--Queens_Canada--NavyNavBackground1.jpg" style="width:100%;height:30px">
 +
</div>
 +
</div></div>
 +
 
 +
 
 +
 
 +
<div class="w3-container" style="padding:5px">
 +
<button onclick="myFunction('Demo6')" class="myButton" style="color:#171A3D;width:100%;">Degradation Rate</button>
 +
<div id="Demo6" class="w3-container w3-hide">
 +
<div style="background-color:#afbee8;color:white;padding:50px 150px 50px 150px;">
 +
<div style="background-color:#afbee8;color:white;padding:50px 150px 50px 150px;">
 +
 
 +
<h1><font color="black" face="Arial"><center><span style="font-weight:normal; font-size: 23pt">Degradation Rates</span></center></font></h1><hr/>
 +
<br>
 +
<br>
 +
 
 +
<p class="big"><font size="5" color="black" face="Corbel">
 +
The degradation rate of mRNA is on the order of 2 to 5 minutes. <br>
 +
The average protein half-life is approximately 23 hours. <br>
 +
<br>
 +
Therefore, degradation rates do not impact curli protein production, as this would imply most of the curli proteins being degenerated during biofilm formation (which can take days). Given this is not the case, and curli protein are fully present in our biofilm, the degradation rate of curli proteins is negligible. 
 +
</font></p>
 +
<br>
 +
</div>
 +
<div style="height:30px;width:100%">
 +
<img src="https://static.igem.org/mediawiki/2017/6/64/T--Queens_Canada--NavyNavBackground1.jpg" style="width:100%;height:30px">
 +
</div>
 +
</div></div>
 +
 
 +
 
 +
 
 +
<div class="w3-container" style="padding:5px">
 +
<button onclick="myFunction('Demo7')" class="myButton" style="color:#171A3D;width:100%;">Anderson Promoter Library</button>
 +
<div id="Demo7" class="w3-container w3-hide">
 +
<div style="background-color:#afbee8;color:white;padding:50px 150px 50px 150px;">
 +
 
 +
 
 +
<h1><font color="black" face="Arial"><center><span style="font-weight:normal; font-size: 23pt">Anderson Promoter Library</span></center></font></h1><hr/>
 +
<br>
 +
<p class="big"><font size="5" face="Corbel" color="black">
 +
The Anderson Promoter Library was utilized by QGEM, given the specific measured promoter strengths, as seen in the table below. By incorporating these known strengths into our ratiometric program (as a factor of transcription rate), QGEM was able to precisely model the outcome ratios of proteins in our biofilm.
 +
<br>
 +
<center>
 +
<img src="https://static.igem.org/mediawiki/2017/7/70/T--Queens_Canada--AndersonPromoterLibraryTable.png" style="width:50%"></center>
 +
<br>
 +
The promoters/parts, BBa_J23101 through BBa_J23119, are a family of constitutive promoters - BBa_J23119 being the consensus promoter sequences. Their sequences simply differ in the -35 and -10 consensus regions.
 +
<br><br>
 +
The promoter strengths listed are relative promoter strengths - hence, having units [RPU]. The relative promoter strength of external promoters, those not found in the Anderson Library, can be measured via a procedure found with the <a href="http://parts.igem.org/Measurement/RPU/Measure">RPU Measurement Kit</a>, provided by iGEM. QGEM tried to utilize this measurement kit, creating our own family of T7 promoters. Unfortunately, the T7 promoter failed the test, and no conclusive measurements were obtained pertaining to RPU strength.
 +
 
 +
</div>
 +
 
 +
 
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 +
<div style="height:30px;width:100%">
 +
<img src="https://static.igem.org/mediawiki/2017/6/64/T--Queens_Canada--NavyNavBackground1.jpg" style="width:100%;height:30px">
 +
</div>
 +
</div></div>
 +
 
 +
</div></div></div>
 +
 
 +
 
 +
 
 +
<br>
 +
<br>
 +
<br>
 +
<br>
 +
<br>
 +
 
 +
<div class = "footer">
 +
  <style>
 +
    .footer { padding: 10px; background-color: #171A3D; }
 +
    .footer > div { width: 500px; margin: 0 auto; padding-top: 50px; }
 +
    .footer > div > img { float: left; height: 100px; display: inline-block; position: relative; margin-left: 6px; margin-right: 6px; }
 +
    .footer > p { text-align: center; color: #ffffff }
 +
    .footer > p > a { color: #ffffff; } <!text  of the "contact us">
 +
  </style>
 +
  <p><font face="Corbel">contact us: <a href="director@qgemteam.com">director@qgemteam.com</a></p></font>
 +
</div>

Latest revision as of 02:47, 31 October 2017

The mathematical modeling theory outlined on this page was integrated in the creation of our application, to ensure reliable results.


Relating Relative Promoter Units to Transcription Rate


Assumption:

The first major assumption, is declaring "Promoter Activity" , to be a direct model of transcription rate. "Promoter Activity" is the number of RNAP molecules that clear the final base pair of a promoter (with units of [PoPS] = Polymerase per second).


Thus,

Where,

Thus, through simple substitution:




The modelling can further be simplified through a series of assumptions:
1) GFP expressed from test and standard promoters, have equivalent maturation rates, as they mature under the same conditions:


2) Since both the test and standard promoters are carried on the same plasmid backbone, assume they have the same average copy number:


3) Since promoters have been standardized to have identical transcription initiation sites (predicted) and identical sequences downstream of the site, we expect them to produce the same mRNA sequences.
Therefore,
Expect transcribed mRNA to be identical, implying mRNA degradation rates are equivalent:


Thus, we assume translational rates of immature GFP from some mRNA are equal:


4) Assume that immature GFP is stable. Therefore, protein degradation is negligable compared to dilution due to cell growth.
Thus:

Thus,

and if

Then,


Therefore, we assume the difference between growth rates of cells containing the test promoter construct and cells containing the standard promoter construct, is negligible compared to the maturation rate of GFP.


Thus, for the purposes of QGEM's modelling;


Relating Transcription Rate to Proteins Produced


Assumption:
CsgA alone and CsgA-fusions (such as CsgA-AFP8 and CsgA-SpyTag) behave similarly in terms of transcription in the cells.

The transcription rate of the CsgA gene is modeled as follows:

where,



Thus, by the stated assumption, the transcription rate of CsgA-fusions can be modeled with the same equation.


RBS Strength to Translation Rate


Altering the RBS strength of the ribosome binding site in a plasmid, can be completed by altering the genetic makeup of the RBS. This was modeled through the utilization of the RBS Calculator created by Dr. Howard Salis, at Penn State University. Using the forward implementation of the calculator, one input's their protein coding sequence, organism, and target translation initiation rate. The calculator then outputs the RBS sequence required to achieve such a translation initiation rate under the conditions outlined.

Translation Rate to Proteins Produced


The effect translation rate has on the protein production, was accounted for in the Salis Lab RBS Calculator Code. Thus, by simply declaring the desired translation initiation rate, the code properly took into account the impacts on protein production.

Is There a Maximum Threshold of Secretion?



Is diffusion the rate limiting step? Do CsgA pile up in the cell?

After 1 second, a spherical particle of radius 10 nanometers, has a displacement of 6.6 micrometers due to Brownian motion in water at room temperature. Determined via;


Assuming this model represents movement of CsgA, diffusion is not the rate limiting step.


Degradation Rates



The degradation rate of mRNA is on the order of 2 to 5 minutes.
The average protein half-life is approximately 23 hours.

Therefore, degradation rates do not impact curli protein production, as this would imply most of the curli proteins being degenerated during biofilm formation (which can take days). Given this is not the case, and curli protein are fully present in our biofilm, the degradation rate of curli proteins is negligible.


Anderson Promoter Library


The Anderson Promoter Library was utilized by QGEM, given the specific measured promoter strengths, as seen in the table below. By incorporating these known strengths into our ratiometric program (as a factor of transcription rate), QGEM was able to precisely model the outcome ratios of proteins in our biofilm.


The promoters/parts, BBa_J23101 through BBa_J23119, are a family of constitutive promoters - BBa_J23119 being the consensus promoter sequences. Their sequences simply differ in the -35 and -10 consensus regions.

The promoter strengths listed are relative promoter strengths - hence, having units [RPU]. The relative promoter strength of external promoters, those not found in the Anderson Library, can be measured via a procedure found with the RPU Measurement Kit, provided by iGEM. QGEM tried to utilize this measurement kit, creating our own family of T7 promoters. Unfortunately, the T7 promoter failed the test, and no conclusive measurements were obtained pertaining to RPU strength.





contact us: director@qgemteam.com